Earlier today I have presented you with these puzzles, prepared by the author of A lot of fuss about numbers, a new book on mathematics in Shakespeare’s day.
1. Hours and hours
How many hours are there in a week? And if you’ve worked it out, can you now figure out how Shakespeare put that number into words? He did this by using only 15 letters, true to his line “Brevity is the soul of wit.”
Solution 168 = “eight count eight” (Bianca calls this number in Othello)
2. Duke of danger
Hazard was a dice game that was one of the most popular pastimes in Elizabethan England. Shakespeare refers to it indirectly several times. Usually two dice were involved, but sometimes three – which raised this question, a particular source of debate at the time.
Three dice are rolled. Which total is the most likely (and therefore a better bet)?
a. Nine
b. Ten
c. Nine and ten are equally likely.
Solution b
There are 27 ways to score 10 and only 25 to score 9, so 10 is the best bet. Common belief among players at the time was that there were only six ways to get 9 (1-2-6, 1-3-5, 1-4-4, 2-2-5, 2-3-4 and 3-3 -3); and six ways to get 10 (1-3-6, 1-4-5, 2-2-6, 2-3-5, 2-4-4 and 3-3-4) so the odds are believed to be equal . Galileo exposed the fallacy in about 1620.
3. Difficult to comprehend
Shakespeare uses all of the following measurements of distance: a mile, a league, a fathom, and a furlong.
Can you list them in order of size?
Solution
1. a league. Although not an official measure, a league is roughly the distance you can walk in an hour, i.e. three miles. (Jules Verne’s “20,000 Leagues Under the Sea” is one of the more absurd book titles, given that the Earth’s diameter is less than 3,000 leagues.)
2. a mile
3. A furlong is 220 yards (about 200m).
4. A fathom is six feet (about 2m
4. Twin twister
The plot of Twelfth Night revolves around non-identical (fraternal) twins Sebastian and Viola. The perfect excuse to bring this classic sibling puzzle to life:
A farmer from the 17th century observes that one of his sheep is pregnant. As all farmers know, lambs arrive as non-identical twins, each with a 50-50 chance of being male or female. The local vet has an Elizabethan ultrasound machine and finds out the sexes of the lambs: “Is it true that at least one of them will be male?” asked the farmer. “Yes, that’s true” replied the vet.
“In that case,” says the farmer, “the other one will most likely be female”. Is the farmer right?
Solution Yes!
There is a 2/3 chance that one of the lambs will be female. If we know that at least one lamb is male, then the possible pairings of the first and second lamb are male-male, male-female, and female-male, and each of these pairings is equally likely. There will be a woman in two of the three scenarios, hence the 2/3 probability.
As an interesting one, Shakespeare himself was the father of twins, Hamnet and Judith – we should not be surprised that they were a boy and a girl.
A lot of fuss about numbers by Rob Eastaway is out on Thursday 18th April and can be bought on the Guardian Bookstore or other online retailers.
I’ve been doing a puzzle here on alternate Mondays since 2015. I’m always on the lookout for great puzzles. If you want to suggest one, email me.
